On Confidence Intervals for Process Capability Indices in a One-Way Random Model

Abstract

In this article, we investigated the bootstrap calibrated generalized confidence limits for process capability indices C _pk for the one-way random effect model. Also, we derived Bissell's approximation formula for the lower confidence limit using Satterthwaite's method and calculated its coverage probabilities and expected values. Then we compared it with standard bootstrap (SB) method and generalized confidence interval method. The simulation results indicate that the confidence limit obtained offers satisfactory coverage probabilities. The proposed method is illustrated with the help of simulation studies and data sets.

Keywords:

• Bissell's formula
• Bootstrap calibration
• Generalized confidence interval
• One-way random effect model
• Process capability index
• Satterthwaite's method

Mathematics Subject Classification:

• Primary 62P30
• Secondary 62F25, 62F40

Acknowledgment

The authors are grateful to the referees and the Editor for their comments and suggestions which helped in improving this paper. The second author acknowledges that financial assistance from the University Grants Commission of India for supporting this research under the Teacher Fellowship Scheme.